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It is now possible to use source terms in Nucleonica’s Decay Engine++. Given the production rate(s) of the source(s) and duration in time, the activity buildup for the parent(s) and daughters (during the production time) is calculated using the Bateman equations with source term(s). At the end of the production time, the source term is switched off and the nuclides decay as described by the Bateman equations with no source(s).
As an example, consider the production of Rn212 at ISOLDE in CERN using 4 hours of beamtime. The produced Rn212 will decay to Po208 which has the potential to contaminate the accelerator.

The diagram shows the buildup of Rn212 and Po208 during the 4h production period. Thereafter, the Rn212 (halflife 24 m) decays leaving the longer-lived Po208 (half-life 2.9 y) in the system.
The Decay Engine++ can also be used in the case of multiple sources. In a first step a nuclide mixture is created containing the quantities of the source components (in Bq, Ci, mole, etc.). Thereafter the Decay Engine++ is used for the mixture. When the “source rate” units are selected (e.g. Bq/s, Ci/s, mole/s etc.), the source terms are interpreted as source rates.
During the development of the Bateman solution for constant source terms, numerical instabilities were observed principally for short production and decay times typically used in practical applications. To overcome these issues a multiple precision mathematic library was introduced into Nucleonica giving the user the opportunity to select the precision of the Decay Engine++ calculations to avoid such numerical instabilities.